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2. Cindy loves coke. She cares about total amount she has. Coke is sold in two sizes: one-liter bottles denoted by x1, and three-liter bottles denoted by x2. The prices are P1 = $2 and P2 = $7 a. Cindy's utility function is given by U(x1, x2) =............…....

2. Cindy loves coke. She cares about total amount she has. Coke is sold in two sizes: one-liter bottles denoted by x1, and three-liter bottles denoted by x2. The prices are P1 = $2 and P2 = $7 a. Cindy's utility function is given by U(x1, x2) =............…....

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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a,b

**Perfect Substitutes Example** 2. Cindy loves coke. She cares about the total amount she has. Coke is sold in two sizes: one-liter bottles denoted by x1, and three-liter bottles denoted by x2. The prices are P1 = $2 and P2 = $7. a. Cindy’s utility function is given by U(x1, x2) = ……………… b. Show graphically Cindy’s optimal point and how you got it. --- *Explanation:* - **Utility Function:** This represents the total satisfaction Cindy derives from consuming different quantities of one-liter and three-liter coke bottles. In this context, because Cindy cares only about the total amount of coke she consumes, the utility function might be a simple sum of the quantities (e.g., U(x1, x2) = x1 + 3x2), assuming linear utility where each liter of coke contributes equally to her utility. - **Graphical Representation:** To find Cindy's optimal point, draw a budget constraint graph, with x1 on the x-axis and x2 on the y-axis. The slope of the budget line is determined by relative prices (-P1/P2). Cindy's optimal consumption point is where her budget line is tangent to her highest attainable indifference curve. This point maximizes her utility given her budget.
Transcribed Image Text:**Perfect Substitutes Example** 2. Cindy loves coke. She cares about the total amount she has. Coke is sold in two sizes: one-liter bottles denoted by x1, and three-liter bottles denoted by x2. The prices are P1 = $2 and P2 = $7. a. Cindy’s utility function is given by U(x1, x2) = ……………… b. Show graphically Cindy’s optimal point and how you got it. --- *Explanation:* - **Utility Function:** This represents the total satisfaction Cindy derives from consuming different quantities of one-liter and three-liter coke bottles. In this context, because Cindy cares only about the total amount of coke she consumes, the utility function might be a simple sum of the quantities (e.g., U(x1, x2) = x1 + 3x2), assuming linear utility where each liter of coke contributes equally to her utility. - **Graphical Representation:** To find Cindy's optimal point, draw a budget constraint graph, with x1 on the x-axis and x2 on the y-axis. The slope of the budget line is determined by relative prices (-P1/P2). Cindy's optimal consumption point is where her budget line is tangent to her highest attainable indifference curve. This point maximizes her utility given her budget.
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